You may note that there are 4 canonical gospels, each with different authors, which all corroborate eachother, with the earliest written around 30 years after Jesus' death - that is, within living memory of the people who witnessed Jesus's miracles. This is precisely why all the towns where Jesus performed miracles were given by name in the gospels, so that a person could go there and corroborate the stories themselves if they had any doubt, because these events would still be in the local conscience of the people who lived there and you could talk to people who witnessed them, or at the least their children or grandchildren. Also, in many cases, the people who were healed were recorded by name as well, so one could even seek out specific families. There are no accounts of Christianity ever being refuted by producing a witness to Jesus' falsity, but in fact many people continued to insist, even under torture and execution, that they had witnessed Jesus or the apostles perform miracles.
In the secular historical scientific community, Jesus' existence is considered to be very uncontroversial, since he appears in Roman sources as well.